An efficient semi-analytical method by using adaptive approach in solving nonlinear schrödinger equations
This paper introduces a novel method called the Adaptive Hybrid Reduced Differential Transform Method (AHRDTM) to solve Nonlinear Schrödinger Equations (NLSEs). This method provides semi-analytical solutions over a longer time frame. It achieves this by producing sub-division intervals of varying le...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English English |
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Semarak Ilmu
2024
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| Online Access: | https://eprints.ums.edu.my/id/eprint/41941/1/ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/41941/2/FULL%20TEXT.pdf |
| _version_ | 1825715950606876672 |
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| author | Abdul Rahman Farhan Sabdin Che Haziqah Che Hussin Arif Mandangan Jumat Sulaiman |
| author_facet | Abdul Rahman Farhan Sabdin Che Haziqah Che Hussin Arif Mandangan Jumat Sulaiman |
| author_sort | Abdul Rahman Farhan Sabdin |
| collection | UMS |
| description | This paper introduces a novel method called the Adaptive Hybrid Reduced Differential Transform Method (AHRDTM) to solve Nonlinear Schrödinger Equations (NLSEs). This method provides semi-analytical solutions over a longer time frame. It achieves this by producing sub-division intervals of varying lengths, distinguishing it from the classical Multistep Reduced Differential Transform Method (MsRDTM). Importantly, the AHRDTM eliminates the necessity for perturbation, linearization, or discretization, providing the benefits of adaptability and reliability. The outcomes exhibit that AHRDTM yields highly efficient solutions for NLSEs. Moreover, the method is simple, significantly reducing the computational workload in solving NLSE problems, and shows promising opportunity for application in diverse complex partial differential equations (PDEs). The efficiency and effectiveness of AHRDTM are demonstrated through tables and graphical representations. |
| first_indexed | 2024-12-09T00:54:00Z |
| format | Article |
| id | ums.eprints-41941 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-12-09T00:54:00Z |
| publishDate | 2024 |
| publisher | Semarak Ilmu |
| record_format | dspace |
| spelling | ums.eprints-419412024-11-18T03:22:06Z https://eprints.ums.edu.my/id/eprint/41941/ An efficient semi-analytical method by using adaptive approach in solving nonlinear schrödinger equations Abdul Rahman Farhan Sabdin Che Haziqah Che Hussin Arif Mandangan Jumat Sulaiman QA150-272.5 Algebra T1-995 Technology (General) This paper introduces a novel method called the Adaptive Hybrid Reduced Differential Transform Method (AHRDTM) to solve Nonlinear Schrödinger Equations (NLSEs). This method provides semi-analytical solutions over a longer time frame. It achieves this by producing sub-division intervals of varying lengths, distinguishing it from the classical Multistep Reduced Differential Transform Method (MsRDTM). Importantly, the AHRDTM eliminates the necessity for perturbation, linearization, or discretization, providing the benefits of adaptability and reliability. The outcomes exhibit that AHRDTM yields highly efficient solutions for NLSEs. Moreover, the method is simple, significantly reducing the computational workload in solving NLSE problems, and shows promising opportunity for application in diverse complex partial differential equations (PDEs). The efficiency and effectiveness of AHRDTM are demonstrated through tables and graphical representations. Semarak Ilmu 2024 Article NonPeerReviewed text en https://eprints.ums.edu.my/id/eprint/41941/1/ABSTRACT.pdf text en https://eprints.ums.edu.my/id/eprint/41941/2/FULL%20TEXT.pdf Abdul Rahman Farhan Sabdin and Che Haziqah Che Hussin and Arif Mandangan and Jumat Sulaiman (2024) An efficient semi-analytical method by using adaptive approach in solving nonlinear schrödinger equations. Semarak International Journal of Fundamental and Applied Mathematics, 2 (1). pp. 1-12. ISSN 3030-5527 https://doi.org/10.37934/sijfam.2.1.112 |
| spellingShingle | QA150-272.5 Algebra T1-995 Technology (General) Abdul Rahman Farhan Sabdin Che Haziqah Che Hussin Arif Mandangan Jumat Sulaiman An efficient semi-analytical method by using adaptive approach in solving nonlinear schrödinger equations |
| title | An efficient semi-analytical method by using adaptive approach in solving nonlinear schrödinger equations |
| title_full | An efficient semi-analytical method by using adaptive approach in solving nonlinear schrödinger equations |
| title_fullStr | An efficient semi-analytical method by using adaptive approach in solving nonlinear schrödinger equations |
| title_full_unstemmed | An efficient semi-analytical method by using adaptive approach in solving nonlinear schrödinger equations |
| title_short | An efficient semi-analytical method by using adaptive approach in solving nonlinear schrödinger equations |
| title_sort | efficient semi analytical method by using adaptive approach in solving nonlinear schrodinger equations |
| topic | QA150-272.5 Algebra T1-995 Technology (General) |
| url | https://eprints.ums.edu.my/id/eprint/41941/1/ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/41941/2/FULL%20TEXT.pdf |
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